Astronomy Chapter 10
To determine the mass of the central object, we must apply Newton's version of Kepler's third law, which requires knowing the orbital period and average orbital distance (semimajor axis) for at least one star. We could consider any of the stars shown in the figure, so let's consider the star with the highlighted orbit (chosen because its dots are relatively easy to distinguish). What is the approximate orbital period of this star?
* 20 yr
Determine the ratio of the mass of 1 cm3cm3 of neutron star material to the mass of Mount Everest (≈ 5 × 10^10 kg).
*10
Look again at the orbit of the star with the highlighted orbit. By comparing the orbit to the scale bar shown on the diagram, you can estimate that this orbit has a semimajor axis of about _____.
*1150 AU
A white dwarf has a mass of about 0.8 MSun and the radius of about 6800 kilometers. Calculate the average density of the white dwarf, in kilograms per cubic centimeter.
*1200 kg/cm^3
When did scientists first detect gravitational waves from mergers of compact objects (pairs of neutron stars or black holes)?
*2015 *The recent detection of gravitational waves has opened a new window on the universe.
What is the Schwarzschild radius of a 10 solar mass black hole?
*30 Km
Based on the measurements discussed in part D, the mass of the central black hole is calculated to be about __________ times that of the Sun.
*4 million *The central object, Sgr A*, is a black hole with a mass about 4 million times that of the Sun.
The following equation, derived from Newton's version of Kepler's third law, allows us to calculate the mass (M) of a central object, in solar masses, from an orbiting object's period (p) in years and semimajor axis (a) in astronomical units: M=a^3/p^2 Using this formula with the values you found in Parts C and D, what is the approximate mass of the central object?
*4 million solar masses.
Which of the following best describes a black hole?
*A place from which the escape velocity exceeds the speed of light. *Because nothing travel faster than light, if light cannot escape, then nothing can escape from within a black hole.
A pulsar is
*A rapidly spinning neutron star that produces radio waves. *Only a neutron star can spin with such short periods as are observed for pulsars without being teared apart.
If you had something the size of a sugar cube that was made of white dwarf matter, it would weigh about as much as
*A truck *A white dwarf has a mass about that of the Sun compressed into a size about that of Earth, which gives it a density of more than a ton per cubic centimeter.
Consider the statement from Part A reading "a 3-solar-mass black hole may be hidden between Jupiter and Saturn." How do we know this statement is not true?
*An object of that mass would disrupt the orbits of the planets in our solar system.
What predicted the existence of gravitational waves?
*Einstein's general theory of relativity. *Einstein predicted the gravitational waves that were directly detected by the LIGO in 2015.
Which of the following statements about electron degeneracy pressure and neutron degeneracy pressure is true?
*Electron degeneracy pressure is the main source of pressure in white dwarfs, while neutron degeneracy pressure is the main source of pressure in neutron stars. *Both types of degeneracy pressure arise for different reasons than the thermal pressure that supports the structures of stars that still have ongoing nuclear fusion.
The boundary from within which light cannot escape from a black hole is called the black hole's __________.
*Event horizon
Consider the statement from Part A reading "the singularity of a black hole has infinite density." Why is this statement in the "unknown" bin?
*General relativity and quantum mechanics give different answers about the nature of singularity.
Consider the portion of the video that starts with the all-sky view of the Milky Way and then zooms in to the galactic center. All of the images except the first two show radio, infrared, or X-ray light. Why don't these images show visible light?
*Interstellar dust in the galactic disk prevents us from seeing the galactic center with visible light.
What makes us think that the star system Cygnus X-1 contains a black hole?
*It emits x-rays as we expect from a system with an accretion disk, but the unseen star in the system is too massive to be a neutron star. *The x-rays tell us that the system contains either a neutron star or a black hole, so if the mass is too big to be a neutron star, then it must be a black hole.
What happens if a white dwarf reaches the 1.4 MSun limit?
*It explodes as a white dwarf supernova. *As a white dwarf closes on the 1.4 MSun limit, its temperature becomes great enough for the ignition of carbon fusion, resulting in the explosion.
What do we mean by the singularity of a black hole?
*It is the center of the black hole, a place of infinite density where the known laws of physics cannot describe the conditions.
What do we mean by the event horizon of a black hole?
*It is the point beyond which neither light nor anything else can escape. *It gets its name because we cannot get any information about events inside the event horizon.
What is a white dwarf?
*It is the remains of a star that ran out of fuel for nuclear fusion. *Once the nuclear fuel runs out, the star can no longer shine; for relatively low-mass stars, gravity then compresses its remaining core into a white dwarf.
Which statement must be true for a rocket to travel from Earth to another planet?
*It must attain escape velocity from Earth. *If it does not have escape velocity, it will either fall back down or orbit Earth.
Consider a binary system of two neutron stars. How should the emission of gravitational waves affect this system?
*It should cause the orbits of the two objects to decay with time.
Imagine that our Sun were magically and suddenly replaced by a black hole of the same mass (1 solar mass). How would Earth's orbit change?
*It would not change; Earth's orbit would remain the same. *Orbits are determined by the strength of gravity, which depends only on mass. Because the Sun's mass did not change, the orbit would not change.
How would a flashing red light appear as it fell into a black hole?
*Its flashes would shift to the infrared part of the spectrum. *Objects in strong gravity experience gravitational redshift, so light that is red would have its wavelength shifted into the infrared part of the spectrum.
From Part B, you know that from afar you'll never see the in-falling rocket cross the event horizon, yet it will still eventually disappear from view. Why?
*Its light will become so redshifted that it will be undetectable.
What is the key observation needed to determine whether the compact object in Part C is a neutron star or a black hole?
*Measure Doppler shifts in the spectrum of the main-sequence star so that you can determine the mass of the compact object.
Astronomers are seeking to obtain an image of the region around the black hole's event horizon with a project called the Event Horizon Telescope. What type of light does this project seek to observe?
*Radio Waves
If you wanted to observe the center of our galaxy, you would need to point a telescope in the direction of the constellation __________.
*Sagittarius
Notice that some of the stars on the diagram are represented by a series of dots that are very close together, while others have their dots farther apart. Keeping in mind that all the stellar positions were measured at approximately one-year intervals, which stars are moving the fastest in their orbits during the time period indicated by the dots?
*The dots farthest apart.
How does this compare to the mass of familiar objects?
*The mass of one cubic centimeter of white dwarf matter is comparable to the mass of a car.
What makes astronomers think that Cygnus X-1 contains a black hole?
*The unseen object orbited by a luminous star is too massive to be a neutron star. *The fact that the unseen, compact companion is too massive to be a neutron star leaves us with the conclusion that it must be a black hole.
What would happen if a white dwarf gained enough mass to reach the 1.4=solar-mass white dwarf limit?
*The white dwarf would explode completely as a white dwarf supernova.
Suppose two neutron stars or two black holes are closely orbiting one another. What do scientists predict will eventually happen to them, and why?
*Their orbits will spiral inward until the two objects merge because of energy lost through gravitational waves. *The gravitational waves carry away energy as predicted by Einstein's general theory of relativity, causing the orbits to decay until they merge.
You've now found that the central object has a mass of about 4 million solar masses but is no more than about 70 AUAU in diameter—which means it cannot be much larger than the size of our planetary system. Why do these facts lead astronomers to conclude that the central object is a black hole?
*There is no known way to pack so much mass into such a small volume without it collapsing into a black hole.
From the viewpoint of an observer in the orbiting rocket, what happens to time on the other rocket as it falls toward the event horizon of the black hole?
*Time runs increasingly slower as the rocket approaches the black hole.
Consider the statement from Part A reading "black holes make up 1% of the mass of the Milky Way Galaxy." Why is this statement in the "unknown" bin?
*We cannot detect all black holes and therefore don't know the percentage of the galaxy's mass they make up.
Explain your reasoning. Part B
*White dwarfs are the remains of low-mass stars, which are far more numerous than high-mass stars.
What is an accretion disk?
*a disk of hot gas swirling rapidly around a white dwarf, neutron star, or black hole. *The hot gas gradually accretes onto the central object.
A typical neutron star is more massive than our Sun and about the size (radius) of __________.
*a small asteroid (10 kilometers in diameter). *This gives them much higher density than white dwarfs.
If we see a nova, we know that we are observing
*a white dwarf in a binary system. *Novae occur when enough amount of matter from a companion star fell on the surface of a white dwarf to cause a burst of fusion.
The maximum mass of a white dwarf is __________.
*about 1.4 times the mass of our Sun. *We call this the white dwarf limit (also known as the Chandrasekhar limit).
If you were inside the rocket that falls toward the event horizon, from your own viewpoint you would __________.
*accelerate as you fall and cross the event horizon completely unhindered.
According to our modern understanding, what is a nova?
*an explosion on the surface of a white dwarf in a close binary system. *It occurs when fresh hydrogen from the accretion disk piles up on the surface.
What is the basic definition of a black hole? Part 2
*an object with gravity so strong that not even light can escape. *The fact that no light can get out of it is what makes it "black".
A typical white dwarf is __________.
*as massive as the Sun but only about as large in size as Earth. *This makes the density of a white dwarf quite high.
If you were inside the rocket that falls toward the event horizon, you would notice your own clock to be running __________.
*at a constant, normal rate as you approach the event horizon.
Why does matter falling toward a white dwarf, neutron star, or black hole in a binary system form an accretion disk?
*because the infalling matter has some angular momentum. *Conservation of the angular momentum causes an increase of the orbital speed as the matter falls toward the central body. Therefore, the falling matter forms a rotating disk.
LIGO detects gravitational waves because the lengths of its arms change as gravitational waves pass by. About how much are these lengths expected to change when LIGO detects gravitational waves from the merger of two neutron stars or two black holes?
*by an amount smaller than the diameter of a proton. *Note that this is a remarkably small change in length, but LIGO is capable of measuring it.
Given such small length changes (as noted in Part D), what can give scientists confidence that they have really detected a gravitational wave signal?
*detecting the same changes at more than one location. *That is why LIGO uses detectors in different locations.
To calculate the dashed orbits from the stellar positions, astronomers had to assume that __________.
*if they observed for many more years, the dots would trace out ellipses.
From Part E you know the mass of the central object. Now consider its size. Based on what you can see in the diagram, you can conclude that the diameter of the central mass is __________.
*no more than about 70 AU
With current technology, we expect to be able to detect (directly) gravitational waves from a binary system of two neutron stars or two black holes __________.
*only from the instant when the two objects merge into one.
The Schwarzschild radius of a black hole depends on __________.
*only the mass of the black hole. *The greater the mass, the larger the Schwarzschild radius.
Pulsars are thought to be __________.
*rapidly rotating neutron stars. *The pulses occur as their magnetic fields sweep by us with each rotation.
As the falling rocket plunges toward the event horizon, an observer in the orbiting rocket would see that the falling rocket __________.
*slows down as it approaches the event horizon and never actually crosses the event horizon.
The first gravitational waves that were detected directly came from
*the merger of two black holes. *Scientists have now also detected gravitational waves from neutron star mergers.
A neutron star is
*the remains of a star that died in a supernova. *During a collapse core supernova, the core of the star often contracts into a neutron star.
What characteristics of the orbiting stars do we need to measure in order to calculate the mass of the central object, Sgr A*?
*their orbital periods and average orbital distances.
A white dwarf is
*what most stars become when they die. *Low-mass stars end their lives as white dwarfs, and low-mass stars are the most common type of stars.
Which kind of these objects do you think is most common in our galaxy? Part A
*white dwarfs
Consider all of the observations shown in the video. Which of the following are reasonable conclusions?
-Gas orbits the radio source called Sgr A*. -There are strong magnetic fields in the central region of the galaxy. -Stars near the galactic center are much closer together than stars around our Sun.
Which of the following accurately describe some aspect of gravitational waves?
-Gravitational waves are predicted to travel through space at the speed of light. -The first direct detection of gravitational waves came in 2015. -The existence of gravitational waves is predicted by Einstein's general theory of relativity. -Gravitational waves carry energy away from their sources of emission.
Which of the following statements about gravitational waves are true?
-The first direct detection of gravitational waves, announced in 2016, came from the LIGO observatory. -The emission of gravitational waves from merging black holes is predicted by Einstein's general theory of relativity. -The emission of gravitational waves from merging black holes is predicted by Einstein's general theory of relativity.
The Chandra X-Ray Observatory has detected X rays from a star system that contains a main-sequence star of spectral type B6. The X-ray emission is strong and fairly steady, and no sudden bursts have been observed. Which of the following statements are reasonable conclusions about this system?
-The main-sequence star orbits either a neutron star or a black hole. -Gas from the main-sequence star makes an accretion disk around another object.
Listed following are several astronomical objects. Rank these objects based on their mass, from largest to smallest. (Be sure to notice that the main-sequence star here has a different spectral type from the one in Part A.)
-a typical black hole (formed in a supernova) -a typical neutron star. -a one-solar-mass white dwarf. -main-sequence of spectral type M. -Jupiter -the Moon
Listed following are several astronomical objects. Rank these objects based on their diameter, from largest to smallest. (Note that the neutron star and black hole in this example have the same mass to make your comparison easier, but we generally expect black holes to have greater masses than neutron stars.)
-main-sequence star of a spectral type A. -Jupiter -a one-solar-mass white dwarf. -the Moon -a two-solar-mass neutron star. -the event horizon of a two-solar-mass black hole.
Listed following are several astronomical objects. Rank these objects based on their density, from highest to lowest.
-the singularity of a black hole. -a typical neutron star. -a one-solar-mass white dwarf. -a main-sequence star.
Complete the following sentences. Use each choice only once.
1. If you tried to visit a ____a black hole in an X-ray binary system____, you would probably be killed by radiation well before you reached the black hole itself. 2. Ignoring any radiation, you could in principle survive the journey across the event horizon of a ____supermassive black hole____. 3.If you tried to fly into a ___10-solar-mass black hole____, you would be killed by tidal forces before you crossed the event horizon.
A typical neutron star has a mass of about 1.5MSun and a radius of 10 kilometers.
7.2*10^11 kg/cm^3
The following items describe observational characteristics that may indicate that an object is either a neutron star or a black hole. Match each characteristic to the correct object; if the characteristic could apply to both types of object, choose the bin labeled "Both neutron stars and black holes."
Neutron Star: -may emit rapid pulses of radio waves. -may be in a binary system that undergoes X-ray bursts. Black Hole: -is detectable only if it is accreting gas from other objects. -can have a mass of 10 solar masses. Both: -may be located in an X-ray binary. -may be surrounded by a supernova remnant..
Each item below describes an observation of a hypothetical supernova. Classify each observation as either "Not surprising" if it fits in with our current understanding of supernovae, or "Surprising" if the observation would cause us to rethink our understanding of supernovae.
Not Surprising: - A white dwarf supernova in a galaxy of only old stars. - Two massive star supernovae occur in the same young star cluster. - A massive star supernova leaves behind no detectable compact object. - A massive star in a binary system explodes. Surprising: - An isolated star like our Sun explodes as a white dwarf supernova. - A young (5 million years) star explodes as a white dwarf supernova.
Each statement below makes a claim about black holes. Based on current scientific understanding of black holes, sort the statements into the correct bin according to whether the statement is: -True (based on current science), meaning that scientists are confident in this statement based on current understanding of gravity (general relativity) and stellar evolution. -Not true, either because it contradicts current scientific theory or is contradicted by observations. -Unknown, meaning the statement makes a claim that may or may not be true, and for which we would need new science or new observations to decide which it is.
True (based on current science): -a black hole can have the mass of a star in a space less than a few kilometers across. -a black hole is an object smaller than its own Schwarzschild radius. -two orbiting black holes can merge and emit gravitational waves. -material from a binary companion can form an X-ray-emitting accretion disk around a black hole. -a black hole can form during a supernova explosion. Not True: -a 3-solar-mass black hole may be hidden between Jupiter and Saturn. -a black hole will suck in any binary companion star. -you would be squashed by gravity at the event horizon of any black hole. -black holes emit x-ray light from within their event horizons. Unknown: -The singularity of a black hole has infinite density. -Black holes make up 1% of the mass of the Milky Way Galaxy.
The following items describe observational characteristics that could indicate that an object is either a white dwarf or a neutron star. Match each characteristic to the correct object.
White Dwarf: -may be surrounded by a planetary nebula. -emits most strongly in visible and ultraviolet. -may be in a binary system that undergoes nova explosions. Neutron Star: -may be in a binary system that undergoes X-ray bursts. -can have a mass of 1.5 solar masses. -may be surrounded by a supernova remnant. -may repeatedly dim and brighten more than once per second.
Listed following are distinguishing characteristics of different end states of stars. Match these to the appropriate consequence of stellar death.
White Dwarf: -supported by electron degeneracy pressure. -typically about the size (diameter) of Earth. -has a mass no greater than 1.4 MSun. -in a binary system, it can explode as a supernova. Neutron Star: -sometimes appears as a pulsar. -usually has a very strong magnetic field. Black Hole: -size defined by its Schwarzschild radius. -viewed from afar, time stops at its event horizon.
Match the items below with the correct type of supernova.
White dwarf supernova: - Can only occur in a binary system. - Spectra always lack strong hydrogen. lines. - Star explodes completely, leaving no compact object behind. - Has a brighter peak luminosity. - Can occur in a very old star cluster. Massive star supernova: - Black hole or neutron star behind. - Can only occur in a galaxy with ongoing star formation.
What is the basic definition of a black hole?
an object with gravity so strong that not even light can escape. *It's "black" because no light can be emitted from within it.
A neutron star is __________.
the remains of a star that died in a massive star supernova (if no black hole was created). *As far as we know, neutron stars form only as the result of iron core collapse in massive star supernovae.
